Controlling processes in food technology by simplifying the canonical form of fitted response surfaces
Second-order response surfaces are often fitted to the results of designed experiments, and the canonical form of such surfaces can greatly help both in interpreting the results and in deciding what action to take on the process under study. A mixing process on pastry dough is described in which it...
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| Veröffentlicht in: | Applied statistics 1999, Vol.48 (1), p.91-101 |
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| container_title | Applied statistics |
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| creator | Gilmour, S. G. Ringrose, T. J. |
| description | Second-order response surfaces are often fitted to the results of designed experiments, and the canonical form of such surfaces can greatly help both in interpreting the results and in deciding what action to take on the process under study. A mixing process on pastry dough is described in which it is desired to simplify the canonical form to make the control of the process more economical, by basing it on only two of the three factors. We give examples where a simplification is possible with minimal loss of accuracy and where it can be seriously misleading, and we outline the features of the response surface that lead to these two situations. A method of improving the simplification by recalculating the constrained canonical axis is proposed. These methods ensure that the mixing process can be controlled by using only two factors without seriously lowering the quality of the pastry. |
| doi_str_mv | 10.1111/1467-9876.00142 |
| format | Article |
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G.</creatorcontrib><creatorcontrib>Ringrose, T. J.</creatorcontrib><title>Controlling processes in food technology by simplifying the canonical form of fitted response surfaces</title><title>Applied statistics</title><description>Second-order response surfaces are often fitted to the results of designed experiments, and the canonical form of such surfaces can greatly help both in interpreting the results and in deciding what action to take on the process under study. A mixing process on pastry dough is described in which it is desired to simplify the canonical form to make the control of the process more economical, by basing it on only two of the three factors. We give examples where a simplification is possible with minimal loss of accuracy and where it can be seriously misleading, and we outline the features of the response surface that lead to these two situations. A method of improving the simplification by recalculating the constrained canonical axis is proposed. These methods ensure that the mixing process can be controlled by using only two factors without seriously lowering the quality of the pastry.</description><subject>Applications</subject><subject>Canonical analysis</subject><subject>Canonical forms</subject><subject>Coefficients</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Exact sciences and technology</subject><subject>Flow velocity</subject><subject>Food</subject><subject>Food engineering</subject><subject>Food industry</subject><subject>Insurance, economics, finance</subject><subject>Mathematics</subject><subject>Moisture content</subject><subject>Pastries</subject><subject>Polynomials</subject><subject>Principal component analysis</subject><subject>Principal components analysis</subject><subject>Probability and statistics</subject><subject>Process control</subject><subject>Reliability, life testing, quality control</subject><subject>Sciences and techniques of general use</subject><subject>Statistical analysis</subject><subject>Statistics</subject><subject>Truncation</subject><issn>0035-9254</issn><issn>1467-9876</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqFUMFu1DAQjRBILIUzFw4-IG5p7dixnSNaQWlZgUpBe7Qcx-568capJwvk73Gaajky0nhsz3tPM68oXhN8TnJcEMZF2UjBzzEmrHpSrE4_T4sVxrQum6pmz4sXAHucg2C2Ktw69mOKIfj-Dg0pGgtgAfkeuRg7NFqz62OIdxNqJwT-MATvphk77iwyuo-9NzpkcDqg6JDz42g7lCwMsQeL4Jiczpovi2dOB7CvHutZ8ePjh-_rT-Xm6-XV-v2mNIw3Vdkx3VWS6oq0nDrRmko4zSi1WIr8ZrJmoiYGt5hL2pFaMGxd1THWNrVp845nxbtFN69yf7QwqoMHY0PQvY1HUFRyLgjlGXixAE2KAMk6NSR_0GlSBKvZTzW7p2b31IOfmXG1MJIdrDnB26D3MQEY9UtRzWQ-ppykaZpc_HzNOeRssiYmajcestbbxzE1ZPtc0r3x8G8E2dC6IhnGFthvH-z0vwnVt9vb9TLpm4W2hzGmE63iEssH1XJpexjtn1Nbp5-KCypqtf1yqW4-X19vt_WN2tC_XRm2rg</recordid><startdate>1999</startdate><enddate>1999</enddate><creator>Gilmour, S. 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J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4692-d4ad283a21b63f7bc27fa433e0873f74854751c0b0683d15740ef2d44b95cb003</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Applications</topic><topic>Canonical analysis</topic><topic>Canonical forms</topic><topic>Coefficients</topic><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Exact sciences and technology</topic><topic>Flow velocity</topic><topic>Food</topic><topic>Food engineering</topic><topic>Food industry</topic><topic>Insurance, economics, finance</topic><topic>Mathematics</topic><topic>Moisture content</topic><topic>Pastries</topic><topic>Polynomials</topic><topic>Principal component analysis</topic><topic>Principal components analysis</topic><topic>Probability and statistics</topic><topic>Process control</topic><topic>Reliability, life testing, quality control</topic><topic>Sciences and techniques of general use</topic><topic>Statistical analysis</topic><topic>Statistics</topic><topic>Truncation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gilmour, S. G.</creatorcontrib><creatorcontrib>Ringrose, T. J.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><jtitle>Applied statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gilmour, S. G.</au><au>Ringrose, T. J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Controlling processes in food technology by simplifying the canonical form of fitted response surfaces</atitle><jtitle>Applied statistics</jtitle><date>1999</date><risdate>1999</risdate><volume>48</volume><issue>1</issue><spage>91</spage><epage>101</epage><pages>91-101</pages><issn>0035-9254</issn><eissn>1467-9876</eissn><coden>APSTAG</coden><abstract>Second-order response surfaces are often fitted to the results of designed experiments, and the canonical form of such surfaces can greatly help both in interpreting the results and in deciding what action to take on the process under study. A mixing process on pastry dough is described in which it is desired to simplify the canonical form to make the control of the process more economical, by basing it on only two of the three factors. We give examples where a simplification is possible with minimal loss of accuracy and where it can be seriously misleading, and we outline the features of the response surface that lead to these two situations. A method of improving the simplification by recalculating the constrained canonical axis is proposed. These methods ensure that the mixing process can be controlled by using only two factors without seriously lowering the quality of the pastry.</abstract><cop>Oxford, UK and Boston, USA</cop><pub>Blackwell Publishers Ltd</pub><doi>10.1111/1467-9876.00142</doi><tpages>11</tpages></addata></record> |
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| identifier | ISSN: 0035-9254 |
| ispartof | Applied statistics, 1999, Vol.48 (1), p.91-101 |
| issn | 0035-9254 1467-9876 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_38667136 |
| source | RePEc; Business Source Complete; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Oxford University Press Journals All Titles (1996-Current); Wiley Online Library All Journals |
| subjects | Applications Canonical analysis Canonical forms Coefficients Eigenvalues Eigenvectors Exact sciences and technology Flow velocity Food Food engineering Food industry Insurance, economics, finance Mathematics Moisture content Pastries Polynomials Principal component analysis Principal components analysis Probability and statistics Process control Reliability, life testing, quality control Sciences and techniques of general use Statistical analysis Statistics Truncation |
| title | Controlling processes in food technology by simplifying the canonical form of fitted response surfaces |
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